One month Ahmad rented 5 movies and 3 video games for a total of \( \$ 31 \). The next month he rented 7 movies and 9 video games for a total of \( \$ 71 \). Find the rental cost for each movie and each video game. Rental cost for each movie: \( \$ \square] \)

We start by letting \( m \) be the rental cost of one movie and \( g \) be the rental cost of one video game. Then, we have the system: \[ \begin{aligned} 5m + 3g &= 31 \quad \text{(1)}\\ 7m + 9g &= 71 \quad \text{(2)} \end{aligned} \] **Step 1. Eliminate one of the variables.** Multiply equation (1) by \( 3 \) to match the coefficient of \( g \) in equation (2): \[ 3(5m + 3g) = 3(31) \] which gives \[ 15m + 9g = 93 \quad \text{(3)} \] **Step 2. Subtract equation (2) from equation (3).** \[ (15m + 9g) - (7m + 9g) = 93 - 71 \] This simplifies to: \[ 8m = 22 \] Solving for \( m \): \[ m = \frac{22}{8} = \frac{11}{4} \quad (\text{or } \$2.75) \] **Step 3. Substitute \( m = \frac{11}{4} \) into equation (1) to solve for \( g \).** \[ 5\left(\frac{11}{4}\right) + 3g = 31 \] Simplify: \[ \frac{55}{4} + 3g = 31 \] Multiply the entire equation by \( 4 \) to eliminate the fraction: \[ 55 + 12g = 124 \] Subtract \( 55 \) from both sides: \[ 12g = 69 \] Solve for \( g \): \[ g = \frac{69}{12} = \frac{23}{4} \quad (\text{or } \$5.75) \] **Final Answer:** Rental cost for each movie: \( \$\frac{11}{4} \) Rental cost for each video game: \( \$\frac{23}{4} \)